If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

Let A = {1,2,3} and B = {x| x is a prime number less than 10}. Find A x B and B x A.

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R₁ = {(3,7), (4,7), (7,10), (8,1)}

A plane is flying at a speed of 500 km per hour. Express the distanced travelled by the plane as function of time t in hours.

If f(x) = x² - 1. Find
i. f o f
ii. f o f o f

Find k, if f(k) = 2k - 1 and f o f(k) = 5.

if m, n are natural numbers , for what values of m, does 2ⁿ x 5^m ends in 5?

If nine times ninth term is equal to the fifteen times fifteenth term, show that six times twenty fourth term is zero.

Find the sum of first 15 terms of the A.P. \(8,7\frac { 1 }{ 4 } ,6\frac { 1 }{ 2 } ,5\frac { 3 }{ 4 } \),....

The houses of a street are numbered from 1 to 49. Senthil’s house is numbered such that the sum of numbers of the houses prior to Senthil’s house is equal to the sum of numbers of the houses following Senthil’s house. Find Senthil’s house number?

Find the sum of first n terms of the G.P
5, -3, \(\frac { 9 }{ 5 } ,-\frac { 27 }{ 25 } \),...,

Find the first term of the G.P. whose common ratio 5 and whose sum to first 6 terms is 46872

Find the least positive value of x such that
98 \(\equiv \)  (x + 4) (mod 5)

Find the sum of the following
6 + 13 + 20 + ...+ 97

Which of the following sequences are in G.P.?
120, 60, 30, 18

Solve x⁴ - 13x² + 42 = 0

Construct a 3 x 3 matrix whose elements are given by
a_ij = |i - 2j|

Find the values of x, y, z if
\(\left[ \begin{matrix} x-3 & 3x-z \\ x+y+7 & x+y+z \end{matrix} \right] =\left[ \begin{matrix} 1 & 0 \\ 1 & 6 \end{matrix} \right] \)

Find the LCM of the given expressions.
(2x² - 3xy)², (4x - 6y)³ ,8x³ - 27y³

Write down the quadratic equation in general form for which sum and product of the roots are given below.
\(-\frac { 3 }{ 5 } ,-\frac { 1 }{ 2 } \)

Solve the following quadratic equations by formula method
3y² - 20y - 23 = 0

If α, β are the roots of the equation 2x² - x - 1 = 0, then form the equation whose roots are
α²β, β²α

Find the values of x, y and z from the following equations.
\(\left[ \begin{matrix} x+y+z \\ x+z \\ y+z \end{matrix} \right] =\left[ \begin{matrix} 9 \\ 5 \\ 7 \end{matrix} \right] \)

Observe Fig and find \(\angle\)P

In Figure, O is the centre of a circle. PQ is a chord and the tangent PR at P makes an angle of 50^o with PQ. Find \(\angle\)POQ,